CN102636664A - Method for dynamically estimating accelerometer resolution - Google Patents

Abstract

The invention discloses a method for dynamically estimating accelerometer resolution. The method comprises the following steps of: finishing the setting of an oblique rotation angle and the uniform-velocity rotation modulation through a double-shaft rotary table so as to realize subdivision of the acceleration of gravity; sampling and digitally storing the electric signal output by the accelerometer; and denoising to extract the signal in a digital filtration mode so as to obtain the output of the accelerometer and further determine the resolution thereof. The accelerometer tested by the method disclosed by the invention has high resolution and strong anti-jamming capability; and the method can be used as a test method for a high-resolution inertial measuring unit and an inertial navigation acceleration sensitive element, and is particularly suitable for testing an accelerometer with resolution being higher than 0.1mu g.

Description

A kind of method of dynamic estimated acceleration meter resolution

Technical field

The present invention relates to a kind of method of dynamic estimated acceleration meter resolution, adopt double axle table at the uniform velocity to rotate modulation and come dynamic estimated acceleration meter resolution, belong to the technical field of measurement and test of Aero-Space high precision inertance element.

Background technology

High-precision accelerometer and gyroscope are high precision navigation critical elements, also are simultaneously the important component parts of forming hi-Fix orientation system and gravity measuring system.Accelerometer is the important component part of Inertial Measurement Unit (IMU), information such as the angular velocity information that utilizes gyroscope output and accelerometer output acceleration information can computing speeds, position, attitude, functions such as the navigation of completion carrier, location.

At present, gravimetry is widely used aspect the civilian and scientific research in resource exploration, solid tide monitoring etc.The appearance of Airborne Gravimetry System makes efficient, large-scale gravimetry become possibility.Aspect resource exploration, require the precision of gravity measuring system to be superior to 1mGal (1mGal=10 ^-5M/s ²=1 μ g).

High-precision accelerometer also is a key element of forming gravity measuring system and gradiometry system, is superior to 1mGal (1mGal=10 in order to realize gravity measuring system ^-5M/s ²=1 μ g) measuring accuracy then requires the resolution of accelerometer to be better than 0.1mGal, and the gradiometry system is higher to the requirement of acceleration measuring accuracy of measurement.This has higher requirement the especially test of high-precision accelerometer resolution for the test of inertia components and parts.The test of accelerometer resolution generally adopts tilt-angle method to segment earth gravity field as input acceleration, greater than 0.5 μ g, can use dividing head to accomplish the segmentation of acceleration of gravity for resolution.For the accelerometer of resolution less than 0.0001 μ g, the universal gravitation that can adopt object to produce is measured as the input acceleration degree.But the test for resolution from 0.0001 μ g to accelerometer the 0.5 μ g does not have good solution.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiency of prior art, a kind of method of dynamic estimated acceleration meter resolution is provided.

Technical solution of the present invention is:

A kind of method of dynamic estimated acceleration meter resolution, step is following:

(1) degree of will speed up meter is installed in and forms a rigid unitary on the double axle table table top that is used for the calibration accelerometer, and the coordinate system that the definition accelerometer is installed is the geographical coordinate system in sky, northeast, is designated as oxyz, and the coordinate system of accelerometer after the oy axle rotates is ox ₁y ₁z ₁, completion is carried out step (2) after installing;

(2) to the inclination rotational angle α of the SF f that is used to gather accelerometer output, double axle table and at the uniform velocity rotation modulation angular speed ω carry out initializing set, make α ∈ [0.01 °, 0.01 °]; F＞30Hz, [30 °/s of ω ∈ [5 °/s, 30 °/s] ∪;-5 °/s], s is second;

(3) make accelerometer with the turning axle oz of said at the uniform velocity rotation modulation angular speed ω around double axle table ₁At the uniform velocity rotation is through formula δ a=(ω/(2 π f)) (α sin (g of β+γ) ₀) calculate the acceleration δ a between the accelerometer output neighbouring sample point, wherein, β is the turning axle oz of accelerometer around double axle table ₁The angle that turns over, γ is the angle between revolving shaft when rotation tangential acceleration of input axis of accelerometer direction and double axle table, g ₀For acceleration of gravity the sky to component;

(4) output valve of accelerometer is carried out digital filtering, the filtering cutoff frequency gets into step (5) afterwards greater than ω/2 π;

(5) according to formula Δ E=K6a _Max=K* (ω/(2 π f)) * α * g ₀With Δ E _P=(E _I+1-E _i) _MaxDifference theory of computation output increment Δ E and the actual output increment Δ of accelerometer E _P

Wherein, K is the scaling ratio of accelerometer, δ a _MaxMaximal value for the theoretical value of accelerometer input variation between the neighbouring sample point; Wherein, K is the scaling ratio of accelerometer, δ a _MaxMaximal value for the theoretical value of accelerometer input variation between the neighbouring sample point; E _I+1And E _iBe the current value of accelerometer in adjacent two sampled points output, Δ E _PGet all E _I+1And E _iThe maximal value of difference, i is a natural number; E ₁Be output current value, E at first sampled point accelerometer ₂Be output current value, by that analogy at second sampled point accelerometer.

(6) if the actual output increment Δ of accelerometer E _PWith the ratio of theoretical output increment Δ E greater than 0.5, then the resolution of accelerometer is δ a _MaxOtherwise, after the size according to the range regulation α that sets in the step (2), return step (3).

When in the said step (1) accelerometer being installed, the input shaft of accelerometer is vertical each other with the turning axle of double axle table.

In the step (4) scope of choosing of filtering cutoff frequency for (1.2* (ω/2 π), 2* (ω/2 π)].

Accelerometer is [0.01 a °, 0.01 °] at installation table top on the double axle table and the angular range between the earth surface level.

The present invention's advantage compared with prior art is:

(1) the present invention adopts that the inclination angle+at the uniform velocity rotation modulation method segments the component of acceleration of gravity more, can confirm the corresponding acceleration change δ a of maximal value of theoretical output increment Δ E easily through SF, rotation angle speed and angle of inclination are set _Max, be easy to realize being superior to 0.1 μ g input acceleration increment.

(2) adopt at the uniform velocity that rotation modulation method segments gravitational acceleration component, be easy to accelerometer output signal and noise separation, signal to noise ratio (S/N ratio) is high, and antijamming capability is strong.

(3) method realizes conveniently, and can test simultaneously many groups accelerometer, and testing efficiency is high.

Description of drawings

Fig. 1 is a workflow diagram of the present invention.

Fig. 2 is coordinate system and the rotation relation synoptic diagram that the present invention relates to.

Fig. 3 is the scheme of installation of accelerometer of the present invention.

Embodiment

The present invention proposes a kind of method of resolution of dynamic estimated acceleration meter, employing is segmented more acceleration of gravity and (is superior to 5 * 10 ^-7G or equivalent angle change and are superior to 0.1 the measure of ") comes dynamic estimated acceleration meter resolution.As shown in Figure 1, its concrete grammar step is described below:

(1) degree of will speed up meter is installed in and forms a rigid unitary on the double axle table table top that is used for the calibration accelerometer.Described double axle table is one of inertia device general purpose test equipment, mainly realizes the position and the speed function of twin shaft.

Fig. 2 has provided accelerometer coordinate system and rotation relation synoptic diagram, accelerometer is installed carried out according to Fig. 3 mounting means.

Among Fig. 2,1 coordinate system installed for accelerometer is the geographical coordinate system in sky, northeast among the definition figure, is designated as oxyz, 2 for the coordinate system after rotating around oy be ox ₁y ₁z ₁, 3 is α for turning over angle, 4 is around oz ₁The angle that turns over is β, and the note coordinate system is ox ₂y ₂z ₂, be called rotating coordinate system.

Provided the mounting means of accelerometer among Fig. 3, the input shaft of accelerometer and turning axle oz ₁Vertical each other, 5 is the installation table top of double axle table in the diagrammatic sketch, and 6 is accelerometer; 7 is the distance of accelerometer quality testing center and rotation center; Be designated as R, 8 is the angle between revolving shaft when rotation tangential acceleration of input axis of accelerometer direction and double axle table, is designated as γ.

Be prone to know coordinate system ox by the derivation of the transformation relation between the coordinate system ₂y ₂z ₂And being transformed between the coordinate system oxyz,

$C_{\mathrm{oxyz}}^{{\mathrm{ox}}_2{y}_2{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000706931100012.png"\; state="\{\{state\}\}">z</figure-callout>}}_2}=C_{{\mathrm{ox}}_1{y}_1{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HSA00000706931100012.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^{{\mathrm{ox}}_2{y}_2{z}_2}{C}_{\mathrm{oxyz}}^{{\mathrm{ox}}_1{y}_1{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HSA00000706931100012.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}=\left[\begin{array}{ccc}\cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}& 0\\ -\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}& 0& -\sin \mathrm{\&alpha;}\\ 0& 1& 0\\ \sin \mathrm{\&alpha;}& 0& \cos \mathrm{\&alpha;}\end{array}\right]$

$=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}& -\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\\ -\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\\ \sin \mathrm{\&alpha;}& 0& \cos \mathrm{\&alpha;}\end{array}\right]---\left(1\right)$

So, acceleration of gravity is at rotating coordinate system ox ₂y ₂z ₂Under component,

${\stackrel{\&RightArrow;}{g}}_{{\mathrm{ox}}_2{y}_2{z}_2}=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}& \sin \mathrm{\&beta;}& -\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\\ -\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}& \cos \mathrm{\&beta;}& \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\\ \sin \mathrm{\&alpha;}& 0& \cos \mathrm{\&alpha;}\end{array}\right]\left[\begin{array}{c}0\\ 0\\ g_0\end{array}\right]=\left[\begin{array}{c}-\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\\ \sin \mathrm{\&alpha;}\sin \mathrm{\&beta;}\\ \cos \mathrm{\&alpha;}\end{array}\right]g_0---\left(2\right)$

Get ox ₂As the input shaft direction, be designated as a at the acceleration that this side up.Because the component on input axis of accelerometer that the angle γ the during rotation of the revolving shaft of input axis of accelerometer direction and double axle table between the tangential acceleration causes is ω ²Rsin γ.So at ox ₂The input component of accelerometer does on the axle,

a＝-sinαcos(β+γ)g ₀+ω ²Rsinγ(3)

Formula (3) is asked for total differential, can get the variable quantity of acceleration input component,

δa＝-δα(cosαcos(β+γ)g ₀)+δβ(sinαsin(β+γ)g ₀)+

δγ(sinαsin(β+γ)g ₀+ω ²Rcosγ)+(4)

2δω(ωRsinγ)+δR(ω ²sinγ)

When α is a low-angle when often being worth, and hypothesis γ, ω, R be normal value, and formula (4) is put in order and can be got so,

δa＝δβ(αsin(β+γ)g ₀)(5)

The variable quantity of acceleration reaches maximal value, and its size is δ β α g ₀

(2) to the inclination rotational angle α of the SF f that is used to gather accelerometer output, double axle table and at the uniform velocity rotation modulation angular speed ω carry out initializing set, make α ∈ [0.01 °, 0.01 °]; F＞30Hz, [30 °/s of ω ∈ [5 °/s, 30 °/s] ∪;-5 °/s], s is second.

(3) make accelerometer with the turning axle oz of said at the uniform velocity rotation modulation angular speed ω around double axle table ₁At the uniform velocity rotation is through formula δ a=(ω/(2 π f)) (α sin (g of β+γ) ₀) calculate the acceleration ε a between the accelerometer output neighbouring sample point, wherein, β is the turning axle oz of accelerometer around double axle table ₁The angle that turns over, γ is the angle between revolving shaft when rotation tangential acceleration of input axis of accelerometer direction and double axle table, g ₀For acceleration of gravity the sky to component;

Suppose that the angle that turns between the neighbouring sample point is δ β, can know δ β=ω/(2 π f), substitution formula (5) can get,

δa＝(ω/(2πf))(αsin(β+γ)g ₀)(6)

(4) digital filtering is carried out in the output of accelerometer, the filtering cutoff frequency gets into step (5) afterwards greater than ω/2 π; The suggestion frequency selection purposes scope be (1.2* (ω/2 π), 2* (ω/2 π)].

(5) according to formula Δ E=K δ a _Max=K* (ω/(2 π f)) * α * g ₀With Δ E _P=(E _I+1-E _i) _MaxDifference theory of computation output increment Δ E and the actual output increment Δ of accelerometer E _P

Wherein, K is the scaling ratio of accelerometer, δ a _MaxMaximal value for the theoretical value of accelerometer input variation between the neighbouring sample point; E _I+1And E _iBe the current value of accelerometer in adjacent two sampled points output, Δ E _PGet all E _I+1And E _iThe maximal value of difference, i is a natural number;

(6) if the actual output increment Δ of accelerometer E _PWith the ratio of theoretical output increment Δ E greater than 0.5, then the resolution of accelerometer is δ a _MaxOtherwise, after the size according to the range regulation α that sets in the step (2), return step (3).

According to the servo linear acceleration measuring method for testing GJB1037A-2004 of single shaft pendulum-type, the ratio of exporting actual increment mean value and desirable output increment mean value when accelerometer promptly satisfies (Δ E greater than 0.5 _P/ Δ E)＞0.5, can think that then the resolution of accelerometer is δ a _MaxOtherwise the adjustment setting value is carried out the estimation of next round resolution.

For example get α=0.0005 °, ω=5 °/s, f=100Hz, π=3.1416, K=1.25mA/g ₀So, theoretical output increment is following,

ΔE＝1.25mA/g ₀*(5*0.0175/(2*3.1416*100))*0.0005*0.0175*g ₀

＝1.25mA/g ₀*(1.218*10 ^-9g ₀)(7)

＝1.52*10 ^-9mA

If accelerometer is at δ a _MaxThe changing value of output is greater than 0.76*10 between corresponding 2 ^-9MA thinks that so the resolution of accelerometer is 1.218*10 ^-9g ₀Otherwise the adjustment setting value is carried out the estimation of next round resolution.

The present invention not detailed description is a technology as well known to those skilled in the art.

Claims (4)

1. the method for a dynamic estimated acceleration meter resolution is characterized in that step is following:

(1) degree of will speed up meter is installed in and forms a rigid unitary on the double axle table table top that is used for the calibration accelerometer, and the coordinate system that the definition accelerometer is installed is the geographical coordinate system in sky, northeast, is designated as oxyz, and the coordinate system of accelerometer after the oy axle rotates is ox ₁y ₁z ₁, completion is carried out step (2) after installing;

(2) to the inclination rotational angle α of the SF f that is used to gather accelerometer output, double axle table and at the uniform velocity rotation modulation angular speed ω carry out initializing set, make α ∈ [0.01 °, 0.01 °]; F＞30Hz, [30 °/s of ω ∈ [5 °/s, 30 °/s] ∪;-5 °/s], s is second;

(3) make accelerometer with the turning axle oz of said at the uniform velocity rotation modulation angular speed ω around double axle table ₁At the uniform velocity rotation is through formula δ a=(ω/(2 π f)) (α sin (g of β+γ) ₀) calculate the acceleration δ a between the accelerometer output neighbouring sample point, wherein, β is the turning axle oz of accelerometer around double axle table ₁The angle that turns over, γ is the angle between revolving shaft when rotation tangential acceleration of input axis of accelerometer direction and double axle table, g ₀For acceleration of gravity the sky to component;

(4) output valve of accelerometer is carried out digital filtering, the filtering cutoff frequency gets into step (5) afterwards greater than ω/2 π;

(5) according to formula Δ E=K δ a _Max=K* (ω/(2 π f)) * a*g ₀With Δ E _P=(E _I+1-E _i) _MaxDifference theory of computation output increment Δ E and the actual output increment Δ of accelerometer E _P

Wherein, K is the scaling ratio of accelerometer, δ a _MaxMaximal value for the theoretical value of accelerometer input variation between the neighbouring sample point; E _I+1And E _iBe the current value of accelerometer in adjacent two sampled points output, Δ E _PGet all E _I+1And E _iThe maximal value of difference, i is a natural number;

(6) if the actual output increment Δ of accelerometer E _PWith the ratio of theoretical output increment Δ E greater than 0.5, then the resolution of accelerometer is δ a _MaxOtherwise, after the size according to the range regulation α that sets in the step (2), return step (3).

2. the method for a kind of dynamic estimated acceleration meter resolution according to claim 1 is characterized in that: when in the said step (1) accelerometer being installed, the input shaft of accelerometer is vertical each other with the turning axle of double axle table.

3. the method for a kind of dynamic estimated acceleration meter resolution according to claim 1 is characterized in that: in the step (4) scope of choosing of filtering cutoff frequency for (1.2* (ω/2 π), 2* (ω/2 π)].

4. the method for a kind of dynamic estimated acceleration meter resolution according to claim 1 is characterized in that: accelerometer is [0.01 a °, 0.01 °] at installation table top on the double axle table and the angular range between the earth surface level.

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